Wetting of liquid-crystal surfaces and induced smectic layering at a nematic-liquid interface : An x-ray reflectivity study

Masafumi Fukuto,* Oleg Gang, Kyle J. Alvine, Benjamin M. Ocko, and Peter S. Pershan Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, USA Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, New York 11973, USA Division of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA Received 17 December 2007; revised manuscript received 6 February 2008; published 14 March 2008


I. INTRODUCTION
Fluid interfaces and films often provide an ideal platform for exploring fundamental aspects of condensed matter.The fluid interfacial phenomena that have been studied extensively for this purpose include wetting ͓1-4͔, surface freezing ͓5͔, and surface layering ͓6-13͔.Surface-induced ordering provides a means to control the molecular orientation in liquid crystals.For example, there is a growing interest in using fluorinated surfaces to align columnar phases of discotic liquid crystals ͓14,15͔.This is motivated, e.g., by the importance of homeotropic ͑normal-to-surface͒ alignment of the columnar director to the development of efficient organic photovoltaic devices ͓14-16͔.In order to facilitate the rational design of alignment surfaces, it is essential to improve our fundamental understanding of how a given interfacial material causes liquid-crystal molecules to adopt a particular orientation.Due to its simplicity and relative lack of defects, the interface between a liquid crystal and an ordinary liquid should be well suited for elucidating the effects of contact material on liquid crystals ͓17͔.
Composite systems involving both liquids and liquid crystals have recently been drawing a great deal of attention.Dispersions of micrometer-scale liquid droplets within nematic films ͓18,19͔ or at nematic-air interfaces ͓20͔ have been used as model systems for studying the interparticle interactions that are mediated by nematic director fields.Inverse systems, i.e., suspensions of nematic droplets in liquids have been studied for their potential as the working component in optoelectronic devices like displays and light shutters ͓21͔.With a goal of developing label-free biosensors, the sensitivity of liquid crystals to boundary conditions has been exploited to optically detect the adsorption of lipids and proteins at nematic-aqueous-buffer interfaces ͓22͔.While liquid-liquid crystal interfaces are an essential feature of all these systems, direct structural measurements of these interfaces have been rather limited ͓17͔.
We present here a synchrotron x-ray reflectivity ͑XR͒ study of bulk liquid crystal surfaces that are coated by thin wetting films of a fluorocarbon liquid.We chose 4-octyl-4Ј-cyanobiphenyl ͑8CB͒ as the liquid-crystalline subphase because smectic layering had already been observed at both vapor and solid ͑but not liquid͒ interfaces of the bulk nematic or isotropic phases of 8CB and related analogs ͓6-13͔.The wetting film was formed by the fluorocarbon perfluoromethylcyclohexane ͑PFMC͒, which has been shown to completely ͑and immiscibly͒ wet the surface of a long-chain hydrocarbon liquid ͓23,24͔.
Our principal objective is to elucidate the effects of a PFMC overlayer on the interface-induced smectic layering behavior of nematic 8CB.In addition to addressing the role of the fluorocarbon in aligning liquid crystals, the present study allows us to examine the behavior of a liquid crystal at * fukuto@bnl.govan interface with a liquid ͓17͔.In particular, interference between the reflections from the liquid-vapor interface and the underlying liquid crystal provides more definitive phase information on the induced smectic order than was available in the previous measurements on the free surface of other liquid crystals ͓7,9,10͔.On the basis of the electron density profiles extracted from XR, we will show that the homeotropic orientation is preferred for the 8CB molecules that are in contact with the fluorocarbon; this in turn induces critical adsorption of smectic layers at the nematic-8CB-PFMC interface.The results will be contrasted with our previous observation that the adsorption of PFMC completely suppresses the surface freezing of an n-alkane ͓23͔.
The second objective is to extend the study of wetting phenomena to those involving a liquid-crystalline subphase.The surface of a liquid crystal near a bulk phase transition provides an opportunity to study how the wetting behavior may be influenced by the variable degree of structural order just below the interface.Our results indicate that PFMC completely wets the 8CB surface and that the thickening of PFMC films with reduced chemical potential is nearly independent of the degree of induced smectic layering on the 8CB side of the interface.
This paper is organized as follows.Section II provides experimental details.Section III presents the results of XR measurements and data analysis ͑Sec.III A͒ and discussions of induced smectic layering ͑Sec.III B͒ and wetting behavior ͑Sec.III C͒.Section IV summarizes the main conclusions.

A. X-ray measurements
X-ray experiments were carried out at beamline X22B of the National Synchrotron Light Source, using the Harvard-BNL liquid surface spectrometer ͓25͔ ͑x-ray wavelength = 1.53 Å͒.The relationship between the horizontal sample surface ͑x-y plane͒ and the scattering angles ͑␣,␤,͒ is illustrated in Fig. 1͑a͒.The difference between the scattered and incident wave vectors defines the wave vector transfer q = k out − k in .Its surface-normal ͑z axis͒ and surface-parallel components are given by q z = k͓sin͑␣͒ + sin͑␤͔͒, q x = k cos͑␤͒sin͑͒, and q y = k͓cos͑␤͒cos͑͒ − cos͑␣͔͒, respectively, where k =2 / .In XR, the intensity I reflected from the surface at the specular condition ͑␤ = ␣, =0; q xy =0͒ is measured as a function of the incident angle ␣ or wave vector transfer q z =2k sin͑␣͒; see Fig. 1͑b͒.Typical detector slit settings corresponded to angular acceptance of ⌬␤ = 0.14°a nd ⌬ = 0.14°, or, equivalently, reciprocal-space resolutions of ⌬q x Ϸ k⌬ = 0.010 Å −1 , ⌬q y Ϸ k sin͑␤͒⌬␤ = ͑q z / 2͒⌬␤ = 0.0013q z , and ⌬q z Ϸ k⌬␤ = 0.010 Å −1 .The reported signal is the difference between the intensity measured at the specular position ͑ =0͒ and the background intensity measured at offsets of b = Ϯ 0.15°.The background-subtracted intensity was normalized to the incident beam to obtain the reflectivity R͑q z ͒ = I͑q z ͒ / I 0 .For the surfaces and settings used in the present study, the contribution of the capillary-wave diffuse scattering to the measured background is insignificant as compared to the specular contribution and therefore neglected in the analysis below.

B. Wetting chamber, materials, and sample preparation
The wetting chamber ͓23,24͔ consisted of two concentric temperature-controlled cells.The hermetically sealed inner copper cell contained the sample ͑PFMC film on a puddle of 8CB͒ in the middle and a bulk reservoir of wetting liquid ͑PFMC͒ at the bottom, such that the surface to be wetted was approximately ϳ50 mm above the cell bottom.The thickness of the wetting film was varied by controlling the temperature difference ⌬T = T − T res Ͼ 0 between the sample and the reservoir ͓23,24,26-29͔, using the setup described in Ref.
The inner cell and internal parts were cleaned as described previously ͓24͔.The DMOAP-coated Pyrex flat was mounted onto a copper disk with a shallow circular trough such that the glass fitted closely in the trough and was pressed against the copper surface for good thermal contact.The copper trough had been cleaned with organic solvents and a 3-min soak in a solution of H 2 SO 4 , HNO 3 , and water ͑20%:10%:70% by volume͒, followed by a thorough rinse with ultrapure water and drying on a heating plate.With the mounted sample holder in place, the sample platform was heated above the nematic-isotropic ͑NI͒ transition temperature T NI Ϸ 40 °C of 8CB ͓13,31-36͔, and roughly 1 g of 8CB was spread over the Pyrex disk using a spatula.This resulted in a puddle of liquid ͑isotropic͒ 8CB, approximately 40 mm in diameter.The cell was then sealed without PFMC and the entire chamber was mounted on the liquid surface spectrometer.The XR measurements were first carried out on the free surface of pure 8CB.
In order to produce saturated vapor needed to form a wetting film, a reservoir of PFMC was introduced, as described previously ͓24͔, by injecting 10 ml of PFMC to the cell bottom.After setting the temperatures, the sample was left undisturbed until the film temperature T and offset ⌬T stabilized, typically for 1-3 h, prior to starting x-ray measurements.At each setting of ͑T , ⌬T ͒, indicated in Fig. 2, two or more XR scans were taken to ensure that the wetting film was stable.
The nematic-smectic-A ͑NA͒ transition temperature T NA is known to drift slowly with time ͓11,37-39͔.Therefore, T NA was checked periodically by heating and cooling the sample across T NA ͑typically at 1-10 mK/min͒ and monitoring the diffracted x-ray intensity of the first Bragg peak at q z = q 0 =2 / d = 0.20 Å −1 , where the smectic layer spacing is d = 31.7 Å for 8CB ͓32,37,40͔.The variations in T NA , determined by the onset of a significant intensity increase upon cooling or the termination of an intensity drop upon heating, were 33.31Ͻ T NA Ͻ 33.47 °C ͑over 36 h͒ and 33.45Ͻ T NA Ͻ 33.48 °C ͑16 h͒ for two preparations of pure 8CB, and 33.73Ͻ T NA Ͻ 33.77 °C ͑40 h͒ and 33.32Ͻ T NA Ͻ 33.33 °C ͑26 h͒ for two preparations of PFMC-coated 8CB.These values agree with the published values of T NA = 33.0-33.9°C for 8CB ͑e.g., ͓13,31-35,37,40͔͒.FIG. 3. ͑a͒ Measured Fresnel-normalized specular reflectivity R / R F vs q z ͑symbols͒, obtained from the free surface of bare 8CB at T − T NA = 0.03, 0.19, 1.4, 9.0, and 20.9 K ͑top to bottom͒, shifted vertically for clarity.The inset shows the linear plot of the same data near the quasi-Bragg peak at q z = q 0 = 0.2 Å −1 .The solid line through each data set represents the best fit from the XR analysis.These XR curves are consistent with the published results ͓7,10͔ for the free surface of nematic 8OCB, an analog of 8CB.͑b͒ The average electron-density profiles ͗͑z͒͘ / ϱ for the 8CB-vapor interface, corresponding to the best-fit R / R F curves in ͑a͒, shifted vertically for clarity.The downward arrow in ͑b͒ indicates the position z 1 = z 0 + d / 4 of the central plane of the first smectic layer.FIG. 4. ͑Color online͒ ͑a͒-͑c͒ Measured Fresnel-normalized reflectivity R / R F vs q z ͑symbols͒, obtained from PFMC-coated surfaces of 8CB at various ⌬T for T − T NA = ͑a͒ 0.7, ͑b͒ 3.7, and ͑c͒ 19.3 K.The solid line through each data set represents the best fit from the XR analysis.͑d͒-͑f͒ The average electron-density profiles ͗͑z͒͘ / ϱ ͑solid lines͒ corresponding to the best-fit R / R F curves in ͑a͒-͑c͒, respectively.In ͑a͒-͑f͒, curves for different ⌬T are shifted vertically for clarity.In ͑d͒-͑f͒, the PFMC and 8CB contributions to ͗͑z͒͘ / ϱ for the highest ⌬T ͑bottommost͒ are indicated by the dashed and dotted lines, respectively, and the downward arrows ͑above the topmost profiles͒ indicate the position z 1 = z 0 + d / 4 of the central plane of the first smectic layer.

A. XR results, analysis, and electron density profiles
Fresnel reflectivity ͓41͔ that would be obtained for an ideally sharp and flat interface for which the electron density changes discontinuously from zero on the vapor side to the bulk average value ϱ ͑= 8CB ͒ of the subphase ͑i.e., 8CB͒.The factor R F , which depends on the critical wave vector q c =4 ͱ r 0 ϱ for total reflection with r 0 denoting the classical electron radius ͓41͔, was calculated by using the T-dependent bulk electron density ϱ ͑T͒ based on the mass density of 8CB ͓33͔.The estimated value of q c is 0.0214 Å −1 just above T NA and decreases with increasing T to 0.0211 Å −1 at the highest probed temperature of T =53 °CϾ T NI .
As shown in Fig. 3͑a͒, the XR data from the bare 8CBvapor interface display a peak at q z = q 0 Ϸ 0.20 Å −1 that grows sharper and larger in amplitude as T − T NA → 0 + .This behavior, similar to the previous observations at the free surface of nematic 4-octyloxy-4Ј-cyanobiphenyl ͑8OCB͒ ͓7,10,11͔, is consistent with the growth of surface-induced smectic layers with a d spacing of d =2 / q 0 Ϸ 31 Å.
The presence of a PFMC layer, by contrast, makes the q z dependence of the XR curves much more complicated, as shown in Figs.4͑a͒-4͑c͒.Qualitatively, the observed R / R F interference patterns can be seen as a superposition of two main features.The first feature is centered at q 0 Ϸ 0.20 Å −1 , has a shape and a sign that depend on ⌬T , and becomes sharper in q z as T − T NA → 0 + .These characteristics are more clearly evident in Fig. 5, showing the T − T NA dependence of R / R F data from the 8CB-PFMC-vapor interface at two different values of ⌬T .Note that the feature at q 0 is a peak or an antipeak for ⌬T =6 K ͓Fig.5͑a͔͒, whereas it is a dip followed by a peak for ⌬T = 1.5 K ͓Fig.5͑b͔͒; in both cases, the feature sharpens as T approaches T NA .The second feature consists of an oscillation in the amplitude of R / R F ͑Kiessig fringes͒ whose period in q z decreases as ⌬T → 0 + .If the feature at q 0 were absent, the R / R F data over 0 Յ q z Յ 0.4 Å −1 ͓Figs.4͑a͒-4͑c͔͒ would contain one oscillation maximum for 0.5Յ⌬T Յ 6 K, two maxima for ⌬T Ϸ 0.05 K, and three maxima for ⌬T Ϸ 0.01 K, regardless of T − T NA .This behavior is consistent with the presence of a wetting layer whose thickness increases with decreasing ⌬T .
The average electron density profile ͗͑z͒͘ along the surface normal has been extracted by fitting model reflectivity curves to the data.The theoretical reflectivity was calculated using ͓42͔ where q t ϵ ͱ q z 2 − q c 2 .Equation ͑1͒ reduces to the well-known Born approximation ͑BA͒ expression ͓41͔ at large q z q c .However, at small q z , Eq. ͑1͒ is equivalent to the low-q z limit of the form based on the distorted-wave Born approximation ͑DWBA͒ for a single fluctuating interface ͓42͔, and therefore provides a more accurate description of R͑q z ͒ than the BA.
The model profile that was used to describe the 8CB-PFMC-vapor interface is given by where the Heaviside step function ⌰͑z − z 0 ͒ is equal to unity for z Ն z 0 and zero for z Ͻ z 0 .The first two terms 1 + 2 are identical to the model used previously ͓10,11͔ to describe the induced smectic layering at the vapor interface.The errorfunction term 1 would describe the subphase-vapor interface in the absence of an adsorbed film.The exponentially decaying sine term 2 accounts for the induced smectic layers, where d is the smectic layer spacing, is the decay length, and A is the amplitude of the density oscillation at z = z 0 .The third term 3 , representing an error-function-based "box" layer, accounts for the presence of the PFMC wetting layer, where L is the layer thickness and L is the layer's electron density relative to the bulk subphase.In order to keep the model as simple as possible, the roughnesses of the 8CB-PFMC and PFMC-vapor interfaces have been set to be equal, so that a single roughness parameter is used in all the error functions in Eq. ͑2͒.Allowing the roughness of the two interfaces to vary independently did not significantly improve the fits.Substituting Eq. ͑2͒ in Eq. ͑1͒, the resulting analytical expression for R / R F has been used to calculate the model reflectivity curves.For the XR data from a pure 8CB surface ͑i.e., in the absence of PFMC͒, five parameters A, d, , z 0 , and were varied in the fitting, with L = 0.For the PFMCcoated 8CB surfaces, six parameters A, d, , z 0 , , and L FIG. 5. Measured R͑q z ͒ / R F ͑q z ͒ from PFMC-coated 8CB ͑sym-bols͒, emphasizing the ͑T − T NA ͒-dependent variation of the feature at q z = 0.2 Å −1 for ⌬T = ͑a͒ 5.2-6.4K and ͑b͒ 1.5 K.The solid line through each data set represents the best fit from the XR analysis.
were varied.In order to minimize the number of free parameters, the relative density L of the wetting layer was kept fixed at the physically expected value of L = PFMC / 8CB = 1.59 ͓43͔, which is approximately independent of T over the probed range of T NA Ͻ T Ͻ 53 °C.For most of the XR data, the data points for q z Ն 0.1 Å −1 were included in the fits.The only exception is that, for the data sets from the PFMC films with the largest probed thickness ͑L Ͼ 40 Å͒, for which R / R F rises steeply just above q c , the fitting range of q z Ն 0.06 Å −1 was used instead.The best-fit R / R F curves for bare and PFMC-coated 8CB surfaces are shown as solid lines in Fig. 3͑a͒  The extracted profiles clearly demonstrate both the presence of interface-induced smectic layers on the liquid-crystal side and their growth as T − T NA → 0 + .Regardless of whether the liquid crystal is in contact with vapor ͓Fig.3͑b͔͒ or with a liquid ͑PFMC͒ film ͓Figs.4͑d͒-4͑f͔͒, the 8CB side of ͗͑z͒͘ / ϱ exhibits an oscillation whose periodicity is essentially equal to the smectic layer spacing of d = 31.7 Å for 8CB ͓32,37,40͔, and the effective number of induced smectic layers, as measured by , increases with decreasing T − T NA .The profiles further indicate that, at each T − T NA , the wetting film thickness grows monotonically as ⌬T → 0 + ͓Figs.4͑d͒-4͑f͒; Table II͔.Together with the apparent insensitivity of T NA to the presence of PFMC ͑Sec.II B͒, the fact that the XR data can be fitted well with the expected value of L TABLE I. List of best-fit parameters for fitting to the XR data for the free surface of bare 8CB in Fig. 3.The electron density profile ͗͑z͒͘ / ϱ was modeled using Eq.͑2͒ with L =0. 3.4Ϯ 0.7 TABLE II.List of best-fit parameters for fitting to the XR data for PFMC-coated surfaces of 8CB in Fig. 4. The electron density profile ͗͑z͒͘ / ϱ was modeled using Eq.͑2͒ with L = 1.59.9.0Ϯ 1.0 6.9Ϯ 0.1 47.4Ϯ 0.9 = 1.59 supports the assumption about the immiscibility between PFMC and 8CB.
The XR data analysis above provides quantitative insights into the induced smectic layering of 8CB ͑through d, , A, and z 0 ͒ and the wetting behavior of PFMC ͑via L͒.These two phenomena are discussed separately in Secs.III B and III C below.We conclude this section with comments on the extracted interfacial roughness .
For a single fluid-fluid interface, the capillary-wave contribution c to the measured roughness is often well approximated by c 2 = ͑k B T / 2␥͒ln͑q max / ⌬q y ͒ ͓24,44͔.The surface tension is ␥ =26 mN/ m for 8CB just above T NA ͓31͔, the upper cutoff wave vector for the shortest allowed capillary wavelength is estimated to be q max = 0.5 Å −1 ͓45͔, and the full width at half maximum ͑FWHM͒ detector resolution ͑Sec.II A͒ can be taken to be ⌬q y = 0.0004 Å −1 at the midpoint q z = 0.3 Å −1 of the typical fitting range.These values yield an estimated capillary roughness of c = 4.4 Å, in good agreement with the extracted values of for the 8CB-vapor interface ͑Table I͒.This demonstrates that the width of the bare 8CB surface is dominated by the capillary roughness and that the intrinsic width is negligible.As for the PFMCcoated 8CB surface, the interpretation of is somewhat ambiguous since the use of this single roughness parameter neglects the fact that the widths of the two interfaces ͑8CB-PFMC and PFMC-vapor͒ are expected to be different ͓24,27͔.Nevertheless, it is physically reasonable that wetting, which lowers the interfacial energy, results in larger values of for the PFMC-coated 8CB ͑Table II͒ than those for the 8CB-vapor interface.Moreover, at each fixed temperature T − T NA , the extracted tends to increase with increasing PFMC thickness L. This behavior is qualitatively consistent with the decoupling of the two interfaces at large separation, which has been shown to result in an enhancement of the capillary roughness at each interface ͓24,27͔.

B. Induced smectic layering at liquid-liquid crystal interfaces
The temperature dependence of the fitted , the surfaceinduced smectic decay length, is plotted in Fig. 6͑a͒, both for the free surface of 8CB and for the PFMC-coated 8CB surface.For comparison, the solid line in the figure represents the longitudinal bulk correlation length ʈ = ʈ,0 ͑T / T NA −1͒ − ʈ = ͑3.8Å͒͑T / T NA −1͒ −0.70 for the smectic order in the nematic phase of 8CB, based on Ref. ͓39͔ ͑also see Refs.͓37,40͔͒.The diverging ʈ ͑T͒ is associated with the nearly second-order nature of the NA transition of 8CB ͓34,37,40͔ and signifies the enhancement of critical fluctuations as T → T NA .
Figure 6͑a͒ shows that, independent of whether the 8CB surface is bare or coated with PFMC, the measured values of are in good agreement with ʈ in terms of both magnitudes and T dependence, except at the smallest probed values of T − T NA Ͻ 0.1 K ͓46͔.The observation ͑T͒Ϸ ʈ ͑T͒ implies that the induced smectic layering at both the 8CB-vapor ͑nematic-vapor͒ and 8CB-PFMC ͑nematic-liquid͒ interfaces is driven by critical adsorption, originating from ͑i͒ the existence of a boundary condition that favors the formation of the first smectic layer and ͑ii͒ the presence of critical fluctuations that leads to the persistence of layering into the bulk material.A similar T-dependent smectic growth behavior has been observed previously at the free surface of an 8CB analog, 8OCB ͓6,7,10,11͔, and at buried interfaces between nematic 8CB and solid substrates ͓8,13͔.
The effects of vapor and PFMC on the boundary conditions of 8CB can be examined further by comparing the amplitude A 1 ϵ A exp͑−d / 4͒Ϸ͗͑z 1 ͒͘ / ϱ − 1 of the smectic density oscillation at the maximum position z 1 ϵ z 0 + d / 4, corresponding to the middle of the first smectic layer ͓Figs.3͑b͒ and 4͑d͒-4͑f͔͒.The amplitude A 1 should serve as a reliable measure of the surface smectic order parameter s in the case of nematic 8CB, for which the induced smectic lay- ers are well defined and extend far from the interface.The extracted A 1 , based on the best-fit parameters ͑A,d,͒, is plotted as a function of T − T NA and ⌬T in Figs.6͑b͒ and 6͑c͒, respectively.On the nematic side ͑T − T NA Ͻ 7 K͒ in Fig. 6͑b͒, the A 1 values for the PFMC-coated 8CB are comparable to those obtained for bare 8CB, within the scatter of the data.For the PFMC-coated nematic 8CB surface, Fig. 6͑c͒ further shows no systematic dependence of A 1 on ⌬T .These observations strongly suggest that the surface order parameter s is independent of whether the nematic 8CB is in contact with vapor or PFMC and remains unchanged no matter how much PFMC liquid is adsorbed, at least up to the maximum probed PFMC thickness of L ϳ 50 Å.This result should be contrasted from the recent study by Lau et al. ͓13͔ of the smectic layer growth at nematic-8CB-solid-substrate interfaces, in which the surface order parameter was found to differ, by as much as a factor of 2, among four different surface treatments of Si/ SiO 2 substrates.
In the smectic-A phase of 8CB, each smectic layer consists of a bilayerlike molecular arrangement such that the cyanobiphenyl head groups segregate toward the central plane of the layer with some degree of overlap and the alkyl tails point away from the central plane, respectively ͓32͔.Thus, the maxima of the density oscillation in the profiles ͗͑z͒͘ ͓Figs.3͑b͒ and 4͑d͒-4͑f͔͒ arise from the segregation of the cyanobiphenyl groups, whereas the minima correspond to the regions rich in the terminal -CH 3 groups.In view of this and Eq.͑2͒, it is significant that the observed offset z 0 roughly satisfies z 0 Ϸ d / 4 ͑Ϸ8 Å; see Tables I and II͒, implying that for both the 8CB-vapor and 8CB-PFMC interfaces the terminal methyl group of 8CB is at the interface ͑z =0͒.This is consistent with the homeotropic ͑normal-to-interface͒ orientation of 8CB molecules at both these interfaces.
It should be noted that the present study provides a more definitive measure of the phase factor z 0 than the previous experiments on other liquid-crystal interfaces ͓7,9,10,13͔.Tables I and II further indicate that the extracted values of z 0 for the 8CB-PFMC interface exhibit less scatter than those for the 8CB-vapor interface.This illustrates one advantage of having a thin, high-contrast overlayer ͑PFMC͒, which makes it possible to obtain reliable phase information on the induced smectic order by exploiting the interference between the scattering from the additional ͑PFMC-vapor͒ interface and the underlying density modulation.
The homeotropic orientation of 8CB at the vapor interface is consistent with the general observation that, for the same number of carbon atoms, n-alkanes exhibit lower surface tensions than aromatic compounds, and that the -CH 3 -terminated surface generally has a lower surface energy than those materials that expose the -CH 2 -groups in the alkyl chain ͓47͔.For example, the surface tension at 20 °C is: ␥ = 18.4 mN/ m for n-hexane CH 3 ͑CH 2 ͒ 4 CH 3 , 25.0 mN/m for cyclohexane ͑CH 2 ͒ 6 , and 28.9 mN/m for benzene C 6 H 6 .Similarly, the observation of the homeotropically aligned 8CB at the interface with PFMC suggests that the minimization of overall interfacial energy favors the terminal -CH 3 groups rather than the -CH 2 -or cyanobiphenyl groups to be in contact with the fluorocarbon.This is one of the main results of the present study and is relevant, e.g., to the increasingly active research on the alignment of the columnar phases of discotic liquid crystals using fluorocarbon surfaces ͓14,15͔.Not unlike 8CB, these diskotic molecules are often composed of an aromatic core and emanating alkyl side chains.
The robustness of induced smectic layering at the PFMC-8CB interface is to be contrasted with our previous study of PFMC-coated surfaces of bulk liquid eicosane ͑C20͒, an n-alkane ͓23,24͔.That study showed that an ultrathin layer of PFMC ͑L ϳ 7 Å͒ was sufficient to completely suppress the surface frozen phase of C20 ͓23͔.The very different effects of a PFMC thin film on the surface ordering behavior of 8CB and C20 reflect the fundamentally different nature of surfaceinduced smectic layering and the surface freezing phenomenon.Unlike the smectic-A layers, which consist of a stacked two-dimensional ͑2D͒ liquid, the surface frozen monolayer of n-alkanes possesses a quasi-long-range 2D positional order.In the case of surface freezing at the air interface ͓5͔, the terminal methyl groups are believed to play the role of a surfactant since the -CH 3 groups have a lower surface energy than the -CH 2 -groups ͓47͔.In turn, this promotes a conformational transition of the alkane chains to the all-trans configuration at a temperature where the underlying bulk remains molten ͓5͔.However, at the PFMC interface, the absence of surface freezing suggests that the adsorption of -CH 3 groups does not significantly lower the surface energy and the bulk and surface freeze at the same temperature.We also note that, at the solid interface, surface freezing of alkanes has never been observed ͓48͔.On the other hand, in the nematic phase of a liquid crystal, the surface-induced smectic layering has the same persistence length as the bulk smectic fluctuations.This suggests that the surface plays the role of fixing the phase of the layering and does not affect the strength of the layering ͑i.e., and A͒.As with alkanes, the methyl groups are at the free surface.However, there is no change in the conformation of the chains associated with the NA transition.Thus, the driving force for the ordering is very different for these two systems.Despite these differences, however, the effect of the PFMC interface is apparently not strong enough to alter the orientational preference that favors the -CH 3 groups at the interface.

C. Wetting of liquid crystal surfaces
The thickness L of the PFMC wetting film on 8CB, obtained from the best fits to the XR data, is plotted as a function of ⌬T in Fig. 7 for the nematic 8CB subphase at T − T NA = 0.7 and 3.7 K and for the isotropic 8CB subphase at T − T NA = 19.3K ͑open symbols͒.For further comparison, Fig. 7 also shows the previously measured data for the thickness of PFMC wetting films on bulk liquid eicosane ͑C20͒ at 37.2 °C ͑filled circles; from Ref. ͓23͔͒.
A major finding of the present study is that the observed thickening behavior of PFMC with decreasing ⌬T is consistent with complete wetting.In order to illustrate this, Fig. 7 shows calculated curves ͑solid and dashed lines͒ for the 1/3 power law behavior L = ͓A eff / ͑6n⌬͔͒ 1/3 ϰ ͑⌬T ͒ −1/3 that is expected for complete wetting films as the bulk liquid-vapor coexistence is approached, i.e., as ⌬ → 0 + for the chemical potential offset ͓1,2͔.These curves are based on ͑i͒ the approximation ⌬ Ϸ͑Q / T͒⌬T ͓26,27͔, ͑ii͒ the known latent heat of vaporization Q and number density n for liquid PFMC ͓49͔, and ͑iii͒ the effective Hamaker constant for the PFMC films on C20, which is estimated from this plot to be A eff = ͑1.5Ϯ0.5͒ ϫ 10 −20 J.For the PFMC films on 8CB, similar graphical inspections yield an estimate of A eff = ͑1.1Ϯ0.4͒ ϫ 10 −20 J for the nematic 8CB and ͑2.3Ϯ 1.0͒ ϫ 10 −20 J for the isotropic 8CB. Figure 7 shows that, within the uncertainties and scatter of the data, the observed ⌬T dependence of L can be described by the 1/3 power law at each T − T NA , especially well for the films on the nematic subphase.
The complete wetting behavior of PFMC is rather robust and largely unaffected by subtle variations in the nature of the subphase.First of all, the PFMC thickness observed for a given ⌬T is not strongly dependent on T − T NA .Figure 7 shows that the thickness L for the isotropic 8CB ͑open circles͒ tends to have slightly higher best-fit values than those for the nematic 8CB ͑open triangles and squares͒.However, for the thickest and thinnest films ͑L Ͼ 40 Å or L Ͻ 10 Å͒, these differences in L are no more than the associated error bars and scatter in the data.It can also be shown that a better agreement between the nematic and isotropic cases is obtained if a more sophisticated approach is used to extract the PFMC thickness from the XR-based density profiles ͓50͔.Similarly, the A eff values estimated above for PFMC on nematic and isotropic 8CB agree with each other within their uncertainties.These observations imply that the amount of PFMC adsorbed on the 8CB surface is not strongly sensitive to the degree of interfacial smectic order, at least up to / d =7-10 smectic layers at T − T NA = 0.7 K ͑Table II͒.This apparent insensitivity may be due to the fact that the van der Waals ͑vdW͒ interactions are long ranged and tend to smear out the effects of ordering at intermolecular length scales.
Second, both the magnitude and the ⌬T dependence of L for the PFMC films on 8CB agree well with those for the PFMC films on C20 ͑Fig.7͒.Evidently, the presence of cyanobiphenyl groups in 8CB does not significantly alter the wetting behavior of PFMC as compared to the case of the alkane C20.This result indicates that, as generally expected ͓51͔, the vdW interactions between PFMC and 8CB are dominated by dispersion forces rather than by those involving the permanent dipole of the cyano group, the effect of which is reduced by the bilayerlike arrangement in the smectic layering.
The magnitudes of A eff estimated above are consistent with the vdW interactions between hydro-and fluorocarbons.With A ij denoting the Hamaker constant for nonretarded vdW interactions between media i and j, A eff for a uniform fluorocarbon film ͑"F"͒ on a uniform hydrocarbon subphase ͑"H"͒ can be approximated as A eff Ϸ A HF − A FF Ϸ ͱ A HH A FF − A FF ͓51͔.In the absence of hydrogen bonds, A ii can be estimated from the surface tension ␥ i of medium i using the relation A ii / ␥ i Ϸ 0.21ϫ 10 −20 J / ͑mN/ m͒ ͓Eq.͑11.35͒ of Ref. ͓51͔͔.Taking ␥ F = 12.5 mN/m for PFMC ͓27͔ and ␥ H =26 mN/m, which is within 1 mN/m of the known surface tensions for bare 8CB ͓31͔ and C20 ͓5͔ at relevant T, the above approximations yield A eff Ϸ 1.2ϫ 10 −20 J, in good agreement with the A eff values estimated from the ⌬T dependence of the PFMC thickness.

IV. SUMMARY
We studied the interfacial structure of the liquid crystal 8CB which was coated by a thin wetting film of an immiscible liquid, the fluorocarbon PFMC.The electron density profile across the 8CB-PFMC-vapor interface was extracted from XR measurements as a function of both the temperature T − T NA of the 8CB subphase above the NA transition and the chemical potential ⌬ ϰ⌬T = T − T res of the PFMC film relative to the bulk liquid reservoir.
The 8CB side of the nematic-liquid ͑8CB-PFMC͒ interface is characterized by critical adsorption of interfaceinduced smectic layers.This is demonstrated by the observation of an electron density modulation whose period is equal to the known smectic layer spacing and whose amplitude decays exponentially toward the nematic subphase.The degree of induced smectic order, as measured by the amplitude decay length , is independent of the amount of adsorbed PFMC.However, the measured increases as the NA transition temperature is approached from above, in quantitative agreement with the longitudinal correlation length ʈ ϰ ͑T − T NA ͒ −0.7 for the smectic fluctuations in the bulk nematic.The results indicate that, just as in the case of the 8CB-vapor interface, the 8CB molecules at the 8CB-PFMC interface are oriented homeotropically such that the terminal methyl groups are at the interface with the fluorocarbon liquid.
The extracted electron density profiles further demonstrate that PFMC completely wets the 8CB surface.The measured thickness of the PFMC wetting film increases with decreasing ⌬T according to the expected power law for FIG. 7. ͑Color online͒ The extracted thickness L of PFMC wetting films on 8CB as a function of ⌬T , obtained from the XR analysis, for PFMC on nematic 8CB at T − T NA = 0.7 ͑open triangles͒ and 3.7 K ͑open squares͒ and on isotropic 8CB at T − T NA = 19.3K ͑open circles͒.The previously measured L for PFMC films on the liquid eicosane ͑C20͒ at T = 37.2 °C is shown as filled circles ͑from Ref. ͓23͔͒.The lines represent the 1/3 power law behavior L ϰ ͑⌬T ͒ −1/3 with an estimated effective Hamaker constant of A eff = ͑1.5Ϯ0.5͒ ϫ 10 −20 J for PFMC on C20.complete wetting, L ϰ ͑⌬T ͒ −1/3 .The wetting behavior of PFMC is nearly independent of the degree of interfacial smectic order in the subphase.The estimated values of the effective Hamaker constant A eff , based on the observed ⌬T dependence of L, are consistent with the dispersion interactions between hydro-and fluorocarbons.
weight and mass density of 8CB ͓33͔, the volume per 8CB molecule is v 0 Ϸ 490 Å 3 / molecule.Assuming that two 8CB molecules occupy a cylindrical volume of 2v 0 = ͑ / 4͒a 2 d where d = 31.7 Å is the smectic layer spacing ͓32,37,40͔, one obtains an estimate of a Ϸ 6 Å or q max Ϸ 0.5 Å −1 .͓46͔ The deviation Ͻ ʈ at T − T NA Ͻ 0.1 K in Fig. 6͑a͒ is likely due to the spread ␦␣ in the incident angle ␣.Taking max = 1000 Å as the saturation value for , the half-width of the sharpest resolvable quasi-Bragg peak in R / R F would be given by ␦q z / 2 Ϸ͑2 / ͒␦␣ Ϸ max −1 , yielding ␦␣ Ϸ 0.24ϫ 10 −3 rad.
In typical XR scans, the incident beam had an angular divergence of ␦␣ 0 = 0.14ϫ 10 −3 rad and a vertical width of 0.05 mm, corresponding to an illuminated footprint length of f =2 mm at q z = q 0 = 0.2 Å −1 .From this, we estimate the radius of curvature at the center of the 8CB surface to be of the order of R Ϸ f / ͑␦␣ − ␦␣ 0 ͒ =20 m.III C͒ implicitly assumes that the average plane of the PFMC-8CB interface is located at z = 0, at which the error function part 1 ͑z͒ + 3 ͑z͒ of the density profile ͓Eq.͑2͔͒ has a locally maximum slope.It is reasonable to question the validity of this assumption for very thin films for which the PFMC contribution to the profile becomes comparable to the overlap with the 8CB contribution ͓Figs.4͑d͒-4͑f͔͒.In view of this, we also extracted the PFMC thickness using an alternative approach that relies not on z = 0 but on the relatively well-defined position z 1 = z 0 + d / 4 for the middle of the first 8CB smectic layer.
The basic steps for this method can be summarized as follows.
͑i͒ The best-fit profile ͗͑z͒͘ / ϱ for the 8CB-PFMC-vapor interface ͓Figs.4͑d͒-4͑f͔͒ was integrated from z =−ϱ ͑vapor͒ to z 1 , to yield ⌫ 8/P/v , where the subscripts 8, P, and v represent 8CB, PFMC and vapor, respectively.͑ii͒ The 8CB contribution to ⌫ 8/P/v was estimated by performing the same integration on the profiles for the 8CB-vapor interfaces ͓Fig.3͑b͔͒, which yields ⌫ 8/v .͑iii͒ An effective PFMC thickness was obtained by defining L eff ϵ͑⌫ 8/P/v − ⌫ 8/v ͒ / L , where L = PFMC / 8CB = 1.59 ͑Sec.III A͒.At each T and ⌬T , L eff thus obtained agrees with the fitting parameter L within their scatter and uncertainties.However, the best-fit values for L eff on the nematic ͑isotropic͒ subphase are slightly higher ͑lower͒ than those for L, resulting in a smaller discrepancy in the PFMC thickness between the two types of subphase than that for L shown in Fig. 7͑c͒.For example, L eff = 21.4Ϯ0.4 Å for the nematic subphase at ͑T − T NA , ⌬T ͒ = ͑0.7 K , 0.16 K͒ and L eff = 23.6Ϯ2.3 Å for the isotropic subphase at ͑19.3 K, 0.18 K͒ agree better than the corresponding values for L ͑Table II͒.These details do not alter the main conclusions about the wetting behavior discussed in Sec.III C. ͓51͔ J. Israelachvili, Intermolecular and Surface Forces ͑Academic, London, 1992͒.
FIG. 1. ͑a͒ Surface x-ray scattering geometry.͑b͒ Specular x-ray reflectivity geometry and an illustration of a wetting film ͑PFMC͒ of thickness L on the surface of a bulk liquid crystal ͑8CB͒ with induced smectic layers of spacing d.The average electron density profile ͗͑z͒͘ along the interface normal is shown on the right.

Figure
Figure 3͑a͒ shows representative normalized XR data ͑symbols͒ for the bare surface of 8CB ͑i.e., no PFMC͒.The data for PFMC wetting films on 8CB at different values of ⌬T are summarized in Figs.4͑a͒-4͑c͒ for T − T NA = 0.7, 3.7, and 19.3 K, respectively.The XR data are shown in terms of the normalized reflectivity R͑q z ͒ / R F ͑q z ͒, where R F ͑q z ͒ is the

FIG. 6 .
FIG.6.͑Color online͒ The extracted decay length of the density oscillation for the induced smectic layering and the oscillation amplitude A 1 = A exp͑−d / 4͒ ͓in units of ͗͑z͒͘ / ϱ ͔ at the center position z 1 = z 0 + d / 4 of the first smectic layer, obtained from the XR analysis.͑a͒ and ͑b͒ A 1 as functions of T − T NA for the 8CB-vapor interface ͑filled circles͒ and the PFMC-coated 8CB ͑open symbols͒, where the vertical dashed line indicates T NI for 8CB.In ͑a͒, the solid line corresponds to the longitudinal bulk correlation length ʈ = ͑3.8Å͒͑T / T NA −1͒ −0.70 for the smectic fluctuations in nematic 8CB ͓39͔, where its extrapolation beyond T NI is shown as the dashed line.͑c͒ A 1 vs ⌬T for PFMC-coated nematic 8CB at T − T NA = 0.7 K ͑open triangles͒ and 3.7 K ͑open squares͒.
and in Figs.4͑a͒-4͑c͒ and 5, respectively, and the corresponding best-fit electron density profiles ͗͑z͒͘ / ϱ are shown in Figs.3͑b͒ and 4͑d͒-4͑f͒.The best-fit parameters for the shown curves are listed in Table I ͑bare 8CB͒ and in Table II ͑PFMC films on 8CB͒.